Thread: homeomorphism help

Hi, learning about homemorphic functions at the moment and am failry confused,

If i have a homeomorphic function h: A - B between two topological spaces A and B,


Is the pre image of the empty set in B the empty set in A ?

let me ask you this: can the pre-image of the empty set in B have ANY elements in it?

Is it that it cant because a homeomorphic function is bijective and continuous?

Look closely at the definition of pre-image: If and the pre-image of under is In other words, for all Now try assuming and see what happens.

i'm sorry i understand the definition but i think i may have some understanding of the empty set missing, obviously this cant happen but why cant a function map something to the empty set and the empty set to something else

Originally Posted by monster

why cant a function map something to the empty set and the empty set to something else

We're not talking about the empty set as an element of or we're talking about it as a subset of and